Abstract
The past two decades has seen new methodological debates on the identification of production function. Olley and Pakes (J Polit Econ 101(6):1149–1164, 1996), Levinsohn and Petrin (Rev Econ Stud 70(2):317–340, 2003), and Ackerberg et al. (Econometrica 83(6):2411–2451, 2015) introduced nonparametric approaches to control for the unobserved productivity in the estimation of production function, which requires the availability of panel data. There has been an another body of the literature that argued that models that are typically estimated on the basis of panel data can also be identified with repeated cross-sections under certain conditions (Verbeek and Vella, 2005). The objective of this paper is two-fold. First, built on the insight of Verbeek and Vella (2005), this paper proposes a new approach to estimate the nonparametric control function based on repeated cross-sections. This is important because in many studies there is a lack of panel data where agents are followed over time, while repeated cross-sections may be available. Second, using cross-sections of Korean ginseng farms over 2006 to 2013, we apply our method to examine the evolution of farm-level productivity over time and across major production regions. Comparing our method with the pooled OLS regressions, the results show that the materials input coefficients are underestimated in the OLS regressions, which is consistent with the data where farms in the large ginseng production regions use relatively less materials than those in the other regions.
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Notes
OP also incorporates the sample selection arising from non-random exit by conditioning on productivity threshold.
Recently, Gandhi et al. (2013) argues that the control function approaches still suffer from the lack of exclusion restriction. Gandhi et al. (2013) suggests to derive additional information from the first order condition of the profit maximization to identify the flexible input coefficient, where the first order condition provides a nonparametric flexible input share regression rather than the control function.
In this paper, we construct the variable adopting the convention used in the literature. For example, Levinsohn and Petrin (2003) constructs intermediate inputs using electricity, materials, and fuels. In Gandhi et al. (2013), intermediate inputs are formed as the sum of raw materials, fuels and electricity, and services. Kasahara and Rodrigue (2008) uses an aggregate measure of domestic and imported materials. The difference is that while the previous studies deflate the expenditures on materials by price indices, in our data we observe physical amount of each of material inputs. Although our construction of materials is based on the literature, this is a rough measure of materials given that there exists a potential heterogeneity in the mix of different material inputs across farms. If the heterogeneity in the mix of material inputs is correlated with the unobserved productivity in the production function, the material coefficient estimates could be biased. The future research should be more careful on the construction of production function variables.
Beyfuss (1999) reports that labor accounts for about 80% of the total cost of ginseng production.
For example, Fezzi and Bateman (2011) models farm profit maximization problem in the presence of fixed amount of allocatable land.
Equation (6) corresponds to the inverse of equation (24) in ACF. While LP uses \({m}_{i(t),t}=m\left({k}_{i(t),t},{\omega }_{i(t),t}\right)\) which is not dependent on \({l}_{i(t),t}\), ACF points out that this specification would lead to the identification problem if labor is also a deterministic function of \({k}_{i(t),t}\) and \({\omega }_{i(t),t}\), and suggests to identify both \({m}_{i(t),t}\) and \({l}_{i(t),t}\) in the second stage of estimation using additional moment conditions.
Bond and Soderbom (2005) argues that OP and LP do not identify parameters in a Cobb-Douglas production function given that if all inputs are chosen optimally and are perfectly flexible, then all inputs are perfectly collinear with the productivity shocks. If some inputs are quasi-fixed and cannot be adjusted corresponding to the current productivity shock, then the remaining variable inputs are linearly dependent on the productivity shock and the quasi-fixed inputs. ACF further discusses these functional dependence problems. ACF shows that OP and LP do not identify the coefficients on variable inputs in the first stage, e.g., labor. While OP and LP invert proxy functions that are unconditional on the labor input, ACF suggests to use investment or material demand functions that are conditional on the labor input.
We use STATA for the estimation. We modify the code provided by Petrin and Poi (2004), which discusses the estimation procedure in detail and introduces the STATA command levpet to estimate standard LP specification.
While this paper is concerned with proposing an idea to estimate the control function approaches based on repeated cross-sections, productivity measurement is also deeply rooted in stochastic frontier analysis. Battese and Rao (2002), Battese et al. (2004), and O’Donnell et al. (2008) provide a framework which allows us to make efficiency comparisons across groups of firms. These studies do this by measuring efficiency relative to metafrontier and group frontier. While metafrontier is defined as the boundary of an unrestricted technology set, group frontiers are defined to be the boundaries of restricted technology sets, where different groups of firms face different restrictions. The metafrontier envelops the group frontiers. Therefore, efficiency of firms measured relative to the metafrontier can be decomposed into two components: a component that measures the distance to the group frontier from a firm’s input-output point, and a component that measures the distance between the group frontier and the metafrontier. The studies provide a technique to estimate metafrontier and group frontiers using stochastic frontier analysis. Furthermore, there is a growing literature addressing the endogeneity in stochastic frontier analysis, e.g., Shee and Stefanou (2015) and Griffiths and Hajargasht (2016).
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Jang, H., Kim, H. & Park, H. Spatiotemporal analysis of Korean ginseng farm productivity. J Prod Anal 53, 69–78 (2020). https://doi.org/10.1007/s11123-019-00560-x
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DOI: https://doi.org/10.1007/s11123-019-00560-x